Magnetic winding and method of making same

ABSTRACT

The present invention provides an improved magnetic winding and method of calculating desired winding parameters (winding layer thickness, number of winding layers and number of turns per winding layer) for a winding in a magnetic component. The invention may be applied to general boundary conditions in a magnetic winding or component and considers relative phase displacement for sinusoidal and nonsinusoidal winding currents. Ratios of magnetic surface field intensities at corresponding inner and outer boundaries of one or more winding layer(s) are calculated, and considered with relative phase displacement to select magnetic winding configurations having desired or optimal power dissipation. In certain aspects, a normalized loss function f(H,R,B,Φ) is utilized to determine a preferred construction among a plurality of iteratively generated selections.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a divisional of co-pending U.S. patentapplication Ser. No. 10/988,240, filed Nov. 12, 2004, which is hereinincorporated by reference.

TECHNICAL FIELD

The present invention relates generally to magnetic components and, morespecifically, to an improved method of calculating or selecting desiredmagnetic winding parameters including winding layer thickness, number ofwinding layers and number of turns per winding layer, and an improvedwound magnetic component such as a coil, inductor, transformer or motorhaving reduced power dissipation.

BACKGROUND OF THE INVENTION

Magnetic and inductive components and devices such as coils, inductors,transformers, motors and others (referred to herein as magneticcomponents) include a winding of one or more of a variety of conductors.Such magnetic components utilize a variety of conductor types includinground, square, or rectangular wire; thin conductor strips or foil;multiple wires twisted together or wound in parallel; various Litz orwoven magnet wire braids (to increase uniformity of current sharingbetween elementary conductors); and various combinations of suchconductor types.

Conventional solenoidal magnetic components comprise winding layerswhich form cylinders around a core. In contrast, planar magneticcomponents utilize conductors and combinations of conductors in anannular configuration. Round, square or rectangular wire, for example,may be wound in annular configurations. In addition, thin conductorstrips or foil may be implemented in annular configurations usingprinted circuit boards, flex circuits, or discrete conductors fabricatedfrom sheet stock, for example, and in other configurations known tothose skilled in the art. In comparison to solenoidal magneticcomponents, the thickness of winding layers and the number of turns perlayer in planar magnetic components, such as those on printed circuitboards, may be varied easily and inexpensively.

FIG. 1 illustrates a cross-section of a winding region or portion in atypical magnetic component having n layers. In FIG. 1, the windinglength of each layer is designated l. The thickness of each windinglayer is designated T₁ through T_(n) and each layer has N_(i) turns,designated N₁ through N_(n). The magnetic surface field intensities atthe inner and outer boundaries of the ith winding layer are designatedas H_(i-1) and H_(i) respectively. The current in the ith winding isdesignated I_(i) and points out of the plane of the paper. When thewinding length l is much greater than the winding layer thickness, themagnetic field distribution is largely parallel to the plane of theconductor in each winding layer. The magnitude ratio of peak magneticsurface field intensities for each conductor layer is defined asfollows: R_(n)=H_(n)/H_(n-1) for each of n layers. Phase shift or phasedisplacement of magnetic surface field intensities for each conductorlayer is defined as: Φ_(n)=φ_(n)−φ_(n-1). The turns in FIG. 1 areillustrated by way of vertical lines in each of the winding layers.

Unless otherwise stated, the following additional definitions withimplied units are used herein:

$\begin{matrix}{H\text{:}\mspace{14mu}{Magnetic}\mspace{14mu}{Field}\mspace{14mu}{Intensity}\text{:}\mspace{14mu}{units}\mspace{14mu}{of}\mspace{14mu}\frac{{Ampere} - {Turn}}{Meter}} \\{{\rho\text{:}\mspace{14mu}{Resistivity}\text{:}\mspace{14mu}{units}\mspace{14mu}{of}\mspace{14mu}{ohm}} - {meter}} \\{{\mu_{0}\text{:}\mspace{14mu}{Permeability}\mspace{14mu}{constant}} = {4\;\pi \times 10^{- 7}\frac{Henry}{Meter}}} \\{f\text{:}\mspace{14mu}{Excitation}\mspace{14mu}{frequency}\text{:}\mspace{14mu}{units}\mspace{14mu}{of}\mspace{14mu} H\; e\; r\; t\; z} \\{{\delta\text{:}\mspace{14mu}{Skin}\mspace{14mu}{Depth}} = \sqrt{\frac{\rho}{\pi\;\mu_{0}f}}}\end{matrix}$

Magnetic components always incur some power dissipation in thewinding(s) and core, which decreases efficiency and increasestemperature. It is generally known that alternating current (AC)conduction generates eddy currents within the conductors of magneticcomponents. Such eddy currents are significant at high frequenciesand/or for large conductor thicknesses. These eddy currents do notcontribute to the macroscopic current of the device, but produce a fieldwhich tends to cancel the external magnetic field produced by the ACcurrent. However, the resultant power dissipation, or loss, and energystorage associated with such eddy currents can have a significant impacton the performance of a magnetic component in an electrical circuit. Inparticular, dissipation from eddy currents can markedly reduce theelectrical efficiency of a system and increase the temperature rise ofthe component. This is due to the well known skin and proximity effects.

Skin effect is the tendency of the current density in a wire to increaseat and near the surface of the wire. In other words, skin effect is thetendency of current in a conductor to flow more toward the surface ofthe conductor as frequency is increased. Current density decaysexponentially inside the conductor, reaching a value at the skin depth(δ) of 1/e times the current density at the surface.

Proximity effect occurs when one conductor is placed in an externalfield generated by one or more other conductors in close proximity. Inthat case, eddy currents are induced in the conductor which oppose thepenetration of the external field. The two eddy current effects occursimultaneously in a conductor carrying an AC current when the conductoris exposed to an external magnetic field. Such eddy currents cause powerdissipation in the windings of magnetic components which increase withfrequency and/or at large conductor thicknesses.

Heretofore, designers of wound magnetic components have utilizedanalytical methods to limit or reduce power dissipation based uponmathematical derivations by P. L. Dowell in 1966 (P. L. Dowell, “Effectsof Eddy Currents in Transformer Windings,” Proceedings of the IEEE, Vol.113, No. 8, August 1966 [incorporated herein by reference]). P. L.Dowell, as with most prior art, assumes a constant layer thickness orheight and does not consider current phase displacement.

High frequency analysis of coil regions has been analyzed using aclassical equivalent foil representation of a winding layer. Thisapproach facilitates an understanding of physics and determination ofconductor boundary conditions. However, this method neglects stray fieldeffects at edges and other asymmetries. Indeed, stray effects can alsoarise from unpredictable manufacturing variables such as insulationbuild up and winding terminations which can cause irregular conductorgeometries.

Increased computing power has facilitated iterative approaches todetermine winding configurations that yield acceptable dissipation. Forexample, Finite Element Analysis has improved mathematical considerationof asymmetries and specific device geometries. Finite Element Analysisis frequently used to determine whether a specific component design isacceptable. It is less valuable, however, in generating or suggestingall potential design parameters and determining an optimal or desiredsolution. Finite Element Analysis software may examine the impact ofvarious configuration parameters such as core type, conductor type andsize and the configuration of terms without the need to build and test aphysical device.

Prior to the present invention, the minimum loss configurations for theindividual winding layers of a magnetic component having more than onelayer was not analytically derived for the general case. M. P. Perry,“Multiple Layer Series Connected Winding Design for Minimal losses,”IEEE Transactions on Power Apparatus and Systems, Vol. PAS-98, No. 1,January/February 1979, pp. 116-123, discloses an analysis for minimizedpower dissipation by choosing specific radial thicknesses for eachwinding layer in a magnetic component. M. P. Perry's analysis is basedon general field solutions for current density distributions in windinglayers of an infinitely long, cylindrical current sheet. Also, Perry'sanalysis assumes a fixed number of turns per layer and zero phasedisplacement. The analysis, therefore, has limited applicability. Inaddition, the stated twelve percent reduction in power dissipation inthe M. P. Perry paper has subsequently been considered too small abenefit when increased manufacturing costs are considered.

Since prior art methods have focused on the equivalent AC resistance ofa complete winding portion or region, the optimization or minimizationof loss in discrete winding layers within a magnetic component has notbeen implemented. As a result, configurations of minimum windingdissipation have been elusive and magnetic components have been lessefficient and larger or hotter in comparison to results for an optimizedconfiguration.

U.S. Pat. Nos. 6,455,971 and 6,758,430 (Palma et al.) disclose anon-random winding technique to reduce proximity losses in motors andother electric machines. U.S. Pat. No. 6,617,665 (Farcy et al.)discloses an optimized width for inductive windings on an integratedcircuit, the width being twice the “skin thickness” corresponding to themaximum frequency of a high frequency current running through thewinding. U.S. Pat. No. 6,650,217 (Wolf et al.) discloses a low profileplanar magnetic component having a stacked winding configuration andspecifying a minimum distance between winding layers and an air gap.U.S. Pat. No. 6,661,326 (Yeh et al.) discloses a wire-winding structureand method to improve transformer power which consists of a method ofwinding wire from a pin on a bobbin around a plurality of slots. U.S.Pat. No. 6,536,701 (Fulton et al.) discloses the use of an improvedformer for winding electrical coils. None of these patents discloses adevice or method having improved winding parameters as in the presentinvention.

Generally, the prior art assumes uniform conductor thickness;approximates dissipation in terms of an equivalent AC/DC resistanceratio for the entire winding portion; and suggests that the best way toreduce winding eddy current loss in a magnetic component is to reducethe number of layers. In addition, none of the prior art accounts forphase displacement in determining preferred winding parameters.

There is a need, therefore, for an improved magnetic component havingdesired or optimal winding parameters including winding layer thickness,number of winding layers and considering variable turns per windinglayer. There is also a need for a cost-effective method of designingand/or manufacturing such magnetic components to reduce powerdissipation. Since multiple transformer secondaries, for example, canhave loads with unequal power factors, or differing nonlinear loads(e.g. independent secondary regulators), and since significantmagnetization currents can occur in primary windings, the harmoniccomponents of winding currents can have significant relative phasedisplacement. It is desirable, therefore, to provide a single method ofdesigning or calculating winding parameters which may be applied togeneral boundary conditions, including consideration for relative phasedisplacement of winding currents.

BRIEF SUMMARY OF THE INVENTION

With reference to the corresponding steps, parts, portions or surfacesof the disclosed embodiment, merely for purposes of illustration and notby way of limitation, the present invention provides an improved methodof determining, calculating and/or designing winding parameters for usein a magnetic component, such as the desired thickness of a windinglayer, the desired number of winding layers and the desired number ofturns in each winding layer. The novel method may be applied to a singlewinding layer in one-layer or multi-layer components, or to any number,or all, of the winding layers in such components. The method can also beapplied to separate and distinct windings that are placed on a givenlayer.

The selection of a desired winding parameter, such as winding layerthickness, turns per layer, or number of layers, in accordance with thisinvention, may result in optimal power dissipation and/or desired powerdissipation given manufacturing constraints such as size, cost,minimum/maximum leakage inductance or minimum/maximum capacitance, orother factors. By improving and/or optimizing conductor thicknesses inall or selected layers of a winding, for example, winding dissipation issignificantly reduced, yielding higher efficiency and a correspondingopportunity for size or temperature rise reduction. As a result, coils,inductors, transformers, motors and various other magnetic components,and the systems which incorporate them can be made smaller and moreefficient in accordance with the present invention, without unduecomplexity or expensive component materials.

As described above, FIG. 1 is a cross sectional view of a winding regionof a magnetic component. AC current within the conductors createsgradients of AC magnetic field within the winding region. These ACmagnetic field gradients apply corresponding magnetic field boundaryconditions to the conductor elements which induce eddy currents whichcan significantly increase dissipation. In certain aspects of theinvention, desired or optimal conductor geometry is determined as afunction of ratio(s) of magnetic field boundary conditions such as peakmagnetic surface field intensities. In other aspects, conductor/windinggeometry is determined as a function of relative phase displacementbetween the magnetic fields at the winding layer boundaries. In oneaspect, the present invention utilizes a determination of optimum ordesired conductor thickness which minimizes winding layer dissipation.In another aspect, this invention specifies the optimum conductorthickness for each layer of the inductive device. Optimum conductorthickness can be implemented, however, on each layer or in selectedlayers based upon preferences (or limitations) in component material andmanufacturing processes.

One aspect of the invention provides the following method of calculatingthe desired thickness of a winding layer for use in a magneticcomponent: determining the magnetic field intensity at the innerboundary or surface of a first winding layer; determining the magneticfield intensity at the outer boundary of the first winding layer;calculating a ratio of the magnetic field intensities; and calculatingthe desired thickness of the first winding layer as a function of thisratio. In certain aspects of the invention, the calculation of a desiredthickness minimizes the normalized power loss function, f(H,R,B,Φ),defined in FIG. 3, wherein B is a ratio of the desired thickness to theskin depth (δ) of a winding layer, R is the ratio of the magnitudes ofopposing peak magnetic surface field intensities, and Φ is the relativephase displacement between the phases of the magnetic fields at theinner and corresponding outer boundaries or surfaces of a given windinglayer. FIG. 2 illustrates such opposing magnetic surface fieldintensities for an example winding layer (10). The normalized lossfunction was generated by finding the general solution of the magneticdiffusion equation. A conductor layer is represented as a semi-infinitecurrent sheet having magnetic field boundary conditions that areparallel to the conductor surface. This assumption is valid at leastwhen winding width, l in FIG. 1, is much larger than winding layerthickness. The application of Maxwell's equations generates thediffusion equation which has been classically solved using imaginaryrepresentations of magnetic field intensity and current density. Trueresults are given by the real components of the imaginary solutions. Thepresent invention is based in part upon a further derivation of P. L.Dowell's loss expressions to enable effective determination of theoptimization function for desired reduced loss configuration(s) for zerophase disparity. Assumed boundary conditions were expanded to encompassphase disparity of magnetic fields and new loss expression(s) and theircorresponding optimization functions derived, whose solutions definedesired reduced or minimized loss configurations.

In certain aspects of the invention, when phase displacement is zero andwinding current is sinusoidal (and R>1), the desired thickness of awinding layer may be calculated in accordance with the expression, cosh(B)=R*cos(B). In another aspect, the calculation of desired thicknesscomprises: computing power dissipation for a plurality of predeterminedthicknesses (e.g. for a selected range, thickness may be varied by aselected increment), which may be limited by manufacturing constraintsor otherwise; and selecting a desired thickness having a desired powerdissipation. In other aspects of the invention, the method contemplatesthat various winding parameters be varied in the same manner. In otheraspects of the invention, the calculation of a desired thickness of awinding layer comprises: plotting the power loss function, f(H,R,B,Φ,for a plurality of predetermined thicknesses; and selecting a desiredthickness having a desired power dissipation. Such predeterminedthicknesses may be generated by a computer or determined manually, forexample.

Another aspect of the invention provides the following: determining themagnetic field intensity at the inner and outer boundaries of a secondwinding layer; calculating a ratio of those magnetic field intensities;and calculating the desired thickness of the second winding layer as afunction of that ratio. The same determinations and calculations may bemade for any number of winding layers and for one, some or all layers ina given component. The desired thickness may minimize the normalizedloss function, f(H,R,B,Φ). In another aspect, the desired thickness of asecond winding layer is calculated in accordance with the expression:cos h(B)=R*cos(B) as defined above. As in a single layer computation,power dissipation may be computed for a plurality of predeterminedthicknesses; and a desired thickness may be selected which has a desiredpower dissipation. Similarly, another aspect of the invention provides amethod by which the power loss function, f(H,R,B,Φ), is plotted for aplurality of predetermined thicknesses of a second (or greater) layer;and a desired thickness is selected which has a desired powerdissipation.

In other aspects, the desired thickness calculated or selected pursuantto the invention is the optimal thickness of the winding layer(s). Inone aspect, the method of this invention includes: manufacturing amagnetic component having such desired thickness. Another aspectprovides a magnetic component having a magnetic winding or windings madeaccording to the method(s) described above. In certain aspects, forsinusoidal winding current corresponding to a situation in which theratio R=0, the desired thickness of the winding layer(s) may becalculated in accordance with the expression: B=π/2. When R=−1 and phasedisplacement is zero, the desired thickness(es) may be calculated inaccordance with the expression: B=π.

In one aspect of the invention, the desired thickness of the firstand/or second winding layer in a winding in a magnetic component iscalculated as a function of the relative phase displacement between thephases of the magnetic fields at the inner and corresponding outerboundary of individual winding layers. One aspect of the inventionprovides the following method of calculating the desired thickness of awinding layer for use in a magnetic component: determining the magneticfield intensity at the inner surface or boundary of a first windinglayer; determining the phase of the magnetic field at the same innerboundary; determining the magnetic field intensity at the outer boundaryor surface of the first winding layer; determining the phase of themagnetic field at the same outer boundary; calculating a ratio of themagnetic field intensities determined and the relative phasedisplacement between the phases of the magnetic fields determined; andcalculating the desired thickness of the first winding layer as afunction of the ratio and the relative phase displacement. In oneaspect, for sinusoidal winding current and cos(Φ)>0, the desiredthickness of a winding layer may be calculated in accordance with theexpression:[R ²+1]/R=[cos(B)/cos h(B)+cos h(B)/cos(B)]*cos(Φ)

For the general case with sinusoidal winding current, the desiredthickness of a winding layer may be calculated in accordance with theexpression:R cos(Φ)sin(B)[sin h(B)[4 cos²(B)+1]+sin h(3B)]−[R²+1] sin(2B)sinh(2B)=0

Each of the foregoing steps may be undertaken, in accordance with thepresent invention, for a second winding layer or any number of windinglayers in the winding of the magnetic component. In certain aspects,power dissipation is computed in accordance with the power lossfunction, and the power loss function may be plotted for a plurality ofpotential winding thicknesses, and a desired thickness selected based onthe plot. The conductor which comprises the winding layer in each aspectof the invention may be round wire, square wire, foil sheet, conductivetape or multiple-strand wire. The thickness of round wires can be takenas

$\sqrt{\frac{\pi}{4}} \star$diameter so that equivalent cross-sectional areas are established forthe purpose of analysis. The invention also includes the step ofmanufacturing a magnetic component (having a magnetic winding) inaccordance with the foregoing steps. A magnetic component which ismanufactured in accordance with the foregoing steps/methods is also partof the present invention.

For nonsinusoidal winding current (which may include a DC component),the invention provides for the determination, through Fourierdecomposition or another method known to those skilled in the art, ofone or more of the harmonic components of the winding current. For oneor more of the harmonic components, calculations may be made of H, theratio R and the relative phase displacement for the inner and outerboundaries of each considered winding layer; and a desired thicknessdetermined from such calculations. Dissipation may be determined as afunction of H, R, B and Φ in accordance with the power loss function. Inanother aspect of the invention, potential winding layer thicknesses areiteratively generated (by computer or otherwise), and a desiredthickness may be selected which has a desired harmonic dissipation. Incertain aspects, similar to the sinusoidal case, the power loss functionis plotted and a desired thickness is selected by computer or byinspection. The foregoing steps may be followed for one, some or allconsidered winding layers.

The present invention also provides for a determination of the followingadditional winding parameters: number of winding layers and number ofturns per layer. In one aspect, the invention provides the followingmethod for calculating such parameters: determining the harmoniccomponents of the winding current; iteratively generating a plurality ofcombinations of one or more of the winding parameters (including windinglayer thickness); for one or more of the harmonic components, computingpower dissipation for a plurality of the generated combinations as afunction of the relative phase displacement and/or as a function of theratio of magnetic surface field intensities between the inner boundaryand the outer boundary of each of the iteratively generated windinglayers; comparing the resulting power dissipations; and selecting adesired combination of winding parameters having desired powerdissipation. The combinations selected may be limited by manufacturingconstraints or specification constraints. As in other aspects of theinvention, power dissipation may be determined in accordance with thepower loss function, f(H,R,B,Φ), and the comparison of resultingdissipations done by plotting the function. These steps may beundertaken for one, some or all considered winding parameters.

In another aspect, the present invention provides for a determination ofwinding thickness, number of winding layers and number of turns perlayer as follows: varying one or more of the winding parameters;determining boundary conditions at the inner boundary and the outerboundary of one or more winding layers for a plurality of combinationsof the varied winding parameters; comparing the boundary conditions atthe inner and outer boundaries; and computing power dissipation as afunction of the relationships between the compared boundary conditions.Each of the foregoing steps and methods may be implemented through acomputer readable medium having computer executable instructions. Suchcomputer readable mediums include without limitation floppy and harddisks, CD-ROM, flash ROM, nonvolatile ROM, DVD, and RAM, for example.

The general object of the invention is to provide a magnetic component(and magnetic winding) having improved, desired or optimal powerdissipation. This improvement can be made in consideration of imposedspecification or manufacturing constraints. It is a further object ofthe present invention to provide a method for determining windingparameters (winding layer thickness, number of layers, number of turnsper layer) for a wound magnetic component having a desired or optimalwinding loss. This desired loss can be achieved in consideration ofimposed specification or manufacturing constraints. Another object is toprovide a method of winding design which is applicable to any type ofcomponent geometry, such as planar transformers, solenoidaltransformers, and motor geometries. Still another object is to provide amethod which may be applied to general boundary conditions, includingconsideration for relative phase displacement of winding currents. Theseand other objects and advantages will become apparent from the foregoingand ongoing written specification, the accompanying drawings and theappended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a cross-sectional view of a winding region of a magneticcomponent.

FIG. 2 is a cross-sectional view of a winding layer of a magneticcomponent.

FIG. 3 is an expression for normalized power loss.

FIG. 4 is a chart illustrating the application of the invention to amagnetic component with three windings.

FIG. 5 is a chart illustrating the application of another embodiment ofthe invention to a magnetic component with two windings.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

At the outset, it should be clearly understood that like referencenumerals are intended to identify the same structural elements, portionsor surfaces consistently throughout the several drawing figures, as suchelements, portions or surfaces may be further described or explained bythe entire written specification, of which this detailed description isan integral part. Unless otherwise indicated, the drawings are intendedto be read (e.g., arrangement of parts, proportion, degree, etc.)together with the specification, and are to be considered a portion ofthe entire written description of this invention. As used in thefollowing description, the terms “horizontal”, “vertical”, “inner”,“outer”, “up” and “down”, as well as adjectival and adverbialderivatives thereof (e.g. “horizontally”, “rightwardly”, “upwardly”,etc.), or similar terms, simply refer to the orientation of theillustrated structure as the particular drawing figure faces the reader.Similarly, the terms “inwardly” and “outwardly” generally refer to theorientation of a surface relative to its axis of elongation, or axis ofrotation, as appropriate.

In a first preferred embodiment of the present invention, correspondingto AC sinusoidal excitation of a magnetic component having a fixednumber of winding layers and a fixed number of turns per winding layer,one or more of the following steps are performed to calculate ordetermine a desired winding layer thickness in one or more magneticwindings:

-   -   a. Identify the current magnitude and phase for each winding in        the magnetic component.    -   b. Using Ampere's Law, calculate the boundary conditions of peak        magnetic surface field intensity and phase at each winding layer        boundary.    -   c. For each winding layer, determine the ratio of opposing peak        magnetic surface field magnitudes (R_(n)) and the relative phase        displacement, Φ_(n)=φ_(n)−φ_(n-1).    -   d. For each winding layer, determine the value of B        (B_(optimum)) which minimizes the loss function, f(H,R,B,Φ), set        forth in FIG. 3. After applying the loss function, optimum or        desired conductor thickness is then equal to B_(optimum)*δ (skin        depth).    -   e. Use one or more of the following methods to find the minimum        or desired values of the loss function:        -   i. Plot f(H,R,B,Φ) as a function of B and find the minimum            by inspection.        -   ii. Use a computer program to calculate the loss function            for a range of potential conductor thicknesses, and select            the conductor thickness which yields minimum or desired loss            function value.        -   iii. For the case of R=0, B_(optimum)=π/2.        -   iv. For the case of R=−1 and Φ=0, B_(optimum)=π.        -   v. For the case of R=1 and Φ=0, B_(optimum)=0 (no            incremental macroscopic current in the conductor layer).        -   vi. For the case of R>1 and Φ=0, determine B using the            equation: cos h(B)=R*cos(B.        -   vii. For the case of R>1 and cos(Φ)>0, determine B using the            equation: [R²+1]/R=[cos(B)/cos h(B)+cos h(B)/cos(B)]*cos(Φ).        -   viii. For the general case, determine B using the function:            R cos(Φ)sin(B)[sin h(B)[4 cos²(B)+1]+sin h(3B)]−[R²+1]            sin(2B)sin h(2B)=0.            B_(optimum) is given by the first positive zero of this            function. In each case, physical and/or manufacturing            constraints, among other things, may affect the selection of            B, and, therefore, winding layer thickness.

FIG. 4 is a chart representing an example of the application of thisembodiment to determine winding layer thickness in a magnetic componenthaving three windings. More specifically, this example relates to atransformer having one primary (Winding 3) and two secondary (Winding 1and Winding 2) windings, with an assumed load current in each secondarywinding of 1 Amp; an assumed primary excitation current at no load of 1Amp; a winding length in each winding of 0.1 m (corresponding to element1 in FIG. 1); six winding layers; and six turns per winding layer.Current phase in Windings 1, 2 and 3 is −1.3, 0.5 and 2.23 radians,respectively, with the phase in Winding 3 derived from assumed values inWindings 1 and 2 in consideration of the no load primary excitationcurrent. From the secondary load currents, the magnitude of the currentin the primary winding (Winding 3), 1.88 Amps, is calculated using thecondition of load Ampere-Turn equivalence to determine the primary loadcurrent component. The total primary current is the vector sum of theprimary load current component and the primary no load excitationcurrent component. B, the ratio between winding layer thickness and skindepth, is initially assumed to be 2. The magnitude and phase of peakmagnetic surface field intensities below and above each layer (H_(below)and H_(above) in FIG. 4) are determined from the following expressions:

$\begin{matrix}{{\overset{\rightarrow}{H}}_{n} = {{\overset{\rightarrow}{H}}_{n - 1} - {\frac{N_{n}}{l}{\overset{\rightarrow}{I}}_{n}}}} \\{{\overset{\rightarrow}{H}}_{0} = \frac{\sum\limits_{i = 1}^{n}\;{N_{i}{\overset{\rightarrow}{I}}_{i}}}{2\; l}}\end{matrix}$wherein {right arrow over (H)}_(n) equals H_(n) cos (ωt+φ_(n)) and{right arrow over (I)}_(n) equals {right arrow over (I)}_(n) cos(ωt+⊖_(n)), ω is the radial frequency and φ_(n) and ⊖_(n) are phasevalues. FIG. 2 illustrates {right arrow over (H)}_(n) for an examplewinding layer 10. Notably, in FIG. 4, the magnitude and phase of themagnetic surface field intensity above Layer Number 1, for example, isequal to the intensity below Layer Number 2, as expected.

The ratio of opposing magnetic surface field intensities(H_(above)/H_(below) in the example) is then computed as well as phaseshift. In the example of FIG. 4, normalized dissipation values are thencomputed for each winding layer. These normalized values are determinedfrom the power loss function, f(H,R,B,Φ), defined in FIG. 4. Thedissipation of each element is referenced to a common value. Therefore,in this example, the normalized dissipation has a value of 100%.

To determine the desired winding layer configuration, the expression instep e.vii. above, for the general case, was plotted. The improved(desired or optimum) value for B was then determined as the value for Bwhich caused the first positive zero of the expression. The bottomportion of the chart in FIG. 4 sets forth the winding layer thicknesses(in terms of B) and related boundary conditions for the improvedmagnetic component. Notably, each winding layer has a differentthickness and the power dissipation is reduced by 16.7 percent. In thisexample, number of layers and turns per layer were held fixed soboundary conditions are unchanged. Further, no specific skin depth waspresented since the utilized expression is not dependent upon skindepth, only B. Although true power is indeed a function of skin depth,actual skin depth is irrelevant because the results in this example aredisplayed in a normalized comparison.

In another preferred embodiment, corresponding to nonsinusoidalexcitation having Fourier harmonic components (which may include DC) andfixed winding layers and a fixed number of turns per winding layer, oneor more of the following steps are performed to determine a desiredwinding layer thickness:

-   -   a. Identify the current waveform for each winding in the        magnetic component.    -   b. Using Fourier decomposition, evaluate the harmonic components        of each current waveform, noting magnitude and phase for each        harmonic component.    -   c. Using computer iteration, vary the thickness of each winding        layer to determine the conductor thickness which minimizes total        harmonic dissipation in each layer.        -   i. Using the respective harmonic components of each winding            current, apply Ampere's Law to evaluate the peak magnetic            surface field intensity and phase at each winding layer            boundary for each harmonic frequency.        -   ii. For each layer, and at each harmonic frequency,            determine the ratio of opposing magnetic surface field            magnitudes and the relative phase displacement.        -   iii. For each layer, calculate the respective harmonic            dissipations using the loss function, f(H,R,B,Φ), applied to            each harmonic boundary condition. For a DC component of            current, I_(DC), in a winding layer of N turns and winding            thickness T, the normalized DC power loss function is:

$f_{DC} = {\frac{1}{T}\left( \frac{N \star I_{DC}}{l} \right)^{2}}$

-   -   -   iv. Calculate the total harmonic dissipation in each layer            by summing the dissipations for each harmonic frequency.        -   v. For each layer, determine the thickness which minimizes            the total harmonic dissipation.            Each of these steps (as with the steps in the other            disclosed embodiments) may be performed with the aid of a            computer, or through computer software or code, and may be            performed manually.

In another preferred embodiment, corresponding to nonsinusoidalexcitation having Fourier harmonic components (including DC) and avariable number of winding layers and a variable number of turns perwinding layer, one or more of the following steps are performed todetermine desired winding parameters comprising winding layer thickness,the number of winding layers and the number of turns per winding layer:

-   -   a. Identify the current waveform for each winding in the        magnetic component.    -   b. Using Fourier decomposition, evaluate the harmonic components        of each current waveform, noting magnitude and phase for each        harmonic component.    -   c. Using computer iteration, vary the number of layers, the        number of turns per layer, and the conductor thickness of each        winding layer to determine the configuration which minimizes        total winding dissipation.        -   i. For each considered combination of winding layer(s) and            number(s) of turns per layer, apply Ampere's Law to evaluate            the magnetic surface field intensity and phase at each            conductor layer boundary for each harmonic frequency, using            the respective harmonic components of each winding current.        -   ii. For each considered winding layer(s) and number(s) of            turns per layer, and at each harmonic frequency, determine            the ratio of opposing surface field magnitudes and the            relative phase displacement.        -   iii. For each considered combination of winding layer(s) and            number(s) of turns per layer, calculate the respective            harmonic dissipations using the loss function, f(H,R,B,Φ),            applied to each harmonic boundary condition. For a DC            component of current, the normalized power loss function is            expressed as f_(DC) above.        -   iv. For each considered combination of layer(s) and            number(s) of turns per layer, calculate the total harmonic            dissipation by summing the dissipations for each harmonic            frequency.        -   v. For each considered combination of layer(s) and number(s)            of turns per layer, determine the thickness which minimizes            the total harmonic dissipation.        -   vi. Evaluate the minimum dissipation for all other            considered combinations of winding layers and number of            turns per layer using this method.        -   vii. Determine the particular winding configuration (number            of layers, respective turns per layer, and respective            conductor layer thicknesses) which yields minimum total            loss. As in each embodiment, the winding parameters selected            may be limited by cost, manufacturing or physical            constraints, or by a specification such as leakage            inductance or capacitance.

FIG. 5 is a chart representing an example of the application of thisembodiment to determine a desired number of winding layers, turns perlayer and winding layer thickness for a transformer having one primary(Winding 2) and one secondary (Winding 1) winding. This problem assumeda variable number of winding layers and turns per winding layer. Theexample also assumed a load current of 1 Amp and a corresponding currentin the primary winding of 1.41 Amps considering an assumed primary noload current of 1 Amp. Winding length l is 0.1 meters. The current phasein Windings 1 and 2 is 0.0 and 2.36 radians, respectively. In thisexample, the method of this embodiment was applied to only one winding(Winding 2). B was initially assumed to be 1.57 for each of two windinglayers. The desired configuration was determined as follows: A specificconfiguration of number of layers and turns per layer was selected. Forthe resultant corresponding boundary conditions of R and Φ, the desiredwinding layer thickness was determined by plotting the expression instep e.vii. The improved (desired or optimum) value for B was determinedas the value for B which caused the first positive zero of theexpression.

The bottom portion of the chart in FIG. 5, labeled “After Improvement,”sets forth the winding layer parameters and related boundary conditionsfor the improved magnetic component, after applying the method of thisembodiment. In this example, power dissipation is improved by 55percent. One significant aspect of the resulting improved configurationis that the number of turns per layer differs in the three resultinglayers, and dissipation is significantly improved. This alonedistinguishes from the prior art.

While there has been described what is believed to be the preferredembodiment of the present invention, those skilled in the art willrecognize that other and further changes and modifications may be madethereto without departing from the spirit of the invention. For example,the method of the present invention may be applied irrespective ofconductor geometry and manufacturing or other physical or costconstraints. Further, all or portions of the inventive method may beapplied to all or portions of a magnetic component. Therefore, theinvention is not limited to the specific details and representativeembodiments shown and described herein. Accordingly, persons skilled inthis art will readily appreciate that various additional changes andmodifications may be made without departing from the spirit or scope ofthe invention, as defined and differentiated by the following claims. Inaddition, the terminology and phraseology used herein is for purposes ofdescription and should not be regarded as limiting.

1. A method of calculating the desired thickness of a winding layer foruse in a magnetic component, comprising: determining the magnetic fieldintensity at the inner boundary of a first winding layer; determiningthe magnetic field intensity at the outer boundary of said first windinglayer; calculating a ratio between said magnetic field intensities; andcalculating the desired thickness of said first winding layer as afunction of said ratio.
 2. The method as set forth in claim 1 whereinsaid desired thickness is calculated in accordance with the expression:cos h(B)=R*cos(B) wherein B is a ratio between said desired thicknessand the skin depth of said first winding layer, and R is said ratiobetween said magnetic field intensities.
 3. The method as set forth inclaim 1, wherein said calculation of said desired thickness comprises:computing power dissipation as a function of said ratio between saidmagnetic field intensities for a plurality of predetermined thicknesses;and selecting a desired thickness having a desired power dissipation. 4.The method as set forth in claim 3 wherein said power dissipation iscomputed in accordance with the power loss function, f(H,R,B,Φ).
 5. Themethod as set forth in claim 1 wherein said calculation of said desiredthickness comprises: plotting the power loss function, f(H,R,B,Φ), for aplurality of predetermined thicknesses; and selecting a desiredthickness having a desired power dissipation.
 6. The method as set forthin claim 1 wherein said desired thickness is the optimal thickness ofsaid first winding layer.
 7. The method as set forth in claim 1, furthercomprising: manufacturing a magnetic component having said desiredthickness.
 8. The method as set forth in claim 1, further comprising:identifying the magnitude of a winding current in said first windinglayer.
 9. The method as set forth in claim 8 wherein said windingcurrent is sinusoidal.
 10. The method as set forth in claim 1 whereinsaid magnetic field intensities are peak magnetic surface fieldintensities.
 11. The method as set forth in claim 1 wherein said windinglayer comprises round wire, square wire, foil sheet, conductive tape ormultiple-strand wire.
 12. A magnetic component made according to themethod of claim
 1. 13. The magnetic component as set forth in claim 12wherein said magnetic component is selected from the group consistingof: coils, inductors, transformers and motors.
 14. The method as setforth in claim 1 wherein said desired thickness is calculated inaccordance with the expression:B=π/2 wherein B is a ratio between said desired thickness and the skindepth of said first winding layer.
 15. The method as set forth in claim1 wherein said desired thickness is calculated in accordance with theexpression:B=π wherein B is a ratio between said desired thickness and the skindepth of said first winding layer.
 16. The method as set forth in claim1, further comprising: determining the magnetic field intensity at theinner boundary of a second winding layer; determining the magnetic fieldintensity at the outer boundary of said second winding layer;calculating a ratio between said magnetic field intensities of saidsecond winding layer; and calculating the desired thickness of saidsecond winding layer as a function of said ratio.
 17. The method as setforth in claim 16 wherein said desired thickness of said second windinglayer is calculated in accordance with the expression:cos h(B)=R*cos(B) wherein B is a ratio between said desired thicknessand the skin depth of said second winding layer, and R is said ratiobetween said magnetic field intensities.
 18. The method as set forth inclaim 16, wherein said calculation of said desired thickness of saidsecond winding layer comprises: computing power dissipation as afunction of said ratio between said magnetic field intensities for aplurality of predetermined thicknesses; and selecting a desiredthickness having a desired power dissipation.
 19. The method as setforth in claim 18 wherein said power dissipation is computed inaccordance with the power loss function, f(H,R,B,Φ).
 20. The method asset forth in claim 16 wherein said calculation of said desired thicknessof said second winding layer comprises: plotting the power lossfunction, f(H,R,B,Φ), for a plurality of predetermined thicknesses; andselecting a desired thickness having a desired power dissipation. 21.The method as set forth in claim 16 wherein said desired thickness isthe optimal thickness of said second winding layer.
 22. The method asset forth in claim 16, further comprising: manufacturing a magneticcomponent having said desired thickness.
 23. A magnetic component madeaccording to the method of claim
 16. 24. The method as set forth inclaim 16 wherein said desired thickness of said second winding layer iscalculated in accordance with the expression:B=π/2 wherein B is a ratio between said desired thickness and the skindepth of said second winding layer.
 25. The method as set forth in claim16 wherein said desired thickness of said second winding layer iscalculated in accordance with the expression:B=π wherein B is a ratio between said desired thickness and the skindepth of said second winding layer.
 26. A method of calculating thedesired thickness of a winding layer for use in a magnetic component,comprising: determining the magnetic field phase at the inner boundaryof a first winding layer; determining the magnetic field phase at theouter boundary of said first winding layer; calculating the relativephase displacement between said phases; calculating the desiredthickness of said first winding layer as a function of said relativephase displacement.
 27. The method as set forth in claim 26 wherein saidcalculation of said desired thickness comprises: computing powerdissipation as a function of said relative phase displacement for aplurality of predetermined thicknesses; and selecting a desiredthickness of said first winding layer having a desired powerdissipation.
 28. The method as set forth in claim 26 wherein saidcalculation of said desired thickness comprises: plotting powerdissipation as a function of said relative phase displacement for aplurality of predetermined thicknesses; and selecting a desiredthickness having a desired power dissipation.
 29. The method as setforth in claim 26, further comprising: manufacturing a magneticcomponent having said desired thickness.
 30. A magnetic component madeaccording to the method of claim
 26. 31. The magnetic component as setforth in claim 30 wherein said magnetic component is selected from thegroup consisting of: coils, inductors, transformers and motors.
 32. Themethod as set forth in claim 26, further comprising: determining themagnetic field phase at the inner boundary of a second winding layer;determining the magnetic field phase at the outer boundary of saidsecond winding layer; calculating the relative phase displacementbetween said phases; calculating the desired thickness of said secondwinding layer as a function of said relative phase displacement.
 33. Themethod as set forth in claim 32 wherein said calculation of said desiredthickness comprises: computing power dissipation as a function of saidrelative phase displacement for a plurality of predeterminedthicknesses; and selecting a desired thickness of said second windinglayer having a desired power dissipation.
 34. The method as set forth inclaim 32 wherein said calculation of said desired thickness comprises:plotting power dissipation as a function of said relative phasedisplacement for a plurality of predetermined thicknesses; and selectinga desired thickness of said second winding layer having a desired powerdissipation.
 35. The method as set forth in claim 32, furthercomprising: manufacturing a magnetic component having said desiredthickness.
 36. A magnetic component made according to the method ofclaim
 32. 37. A method of calculating the desired thickness of a windinglayer for use in a magnetic component, comprising: determining themagnetic field intensity at the inner boundary of a first winding layer;determining the magnetic field phase at the inner boundary of said firstwinding layer; determining the magnetic field intensity at the outerboundary of said first winding layer; determining the magnetic fieldphase at the outer boundary of said first winding layer; calculating aratio between said magnetic field intensities; calculating the relativephase displacement between said phases; and calculating the desiredthickness of said first winding layer as a function of said ratio andsaid relative phase displacement.
 38. The method as set forth in claim37 wherein said desired thickness is calculated in accordance with theexpression:[R ²+1]/R=[cos(B)/cos h(B)+cos h(B)/cos(B)]*cos(Φ) wherein B is a ratiobetween said desired thickness and the skin depth of said first windinglayer, R is said ratio between said magnetic field intensities, and Φ issaid relative phase displacement.
 39. The method as set forth in claim37, wherein said calculation of said desired thickness comprises:computing power dissipation as a function of said ratio between saidmagnetic field intensities for a plurality of predetermined thicknesses;and selecting a desired thickness having a desired power dissipation.40. The method as set forth in claim 39 wherein said power dissipationis computed in accordance with the power loss function, f(H,R,B,Φ). 41.The method as set forth in claim 37, wherein said calculation of saiddesired thickness comprises: computing power dissipation as a functionof said relative phase displacement for a plurality of predeterminedthicknesses; and selecting a desired thickness having a desired powerdissipation.
 42. The method as set forth in claim 41 wherein said powerdissipation is computed in accordance with the power loss function,f(H,R,B,Φ).
 43. The method as set forth in claim 37, wherein saidcalculation of said desired thickness comprises: computing powerdissipation as a function of said ratio between said magnetic fieldintensities and said relative phase displacement for a plurality ofpredetermined thicknesses; and selecting a desired thickness having adesired power dissipation.
 44. The method as set forth in claim 43wherein said power dissipation is computed in accordance with the powerloss function, f(H,R,B,Φ).
 45. The method as set forth in claim 37wherein said calculation of said desired thickness comprises: plottingthe power loss function, f(H,R,B,Φ), for a plurality of predeterminedthicknesses; and selecting a desired thickness having a desired powerdissipation.
 46. The method as set forth in claim 37 wherein saiddesired thickness is the optimal thickness of said first winding layer.47. The method as set forth in claim 37, further comprising:manufacturing a magnetic component having said desired thickness. 48.The method as set forth in claim 37, further comprising: identifying themagnitude and phase of a winding current in said first winding layer.49. The method as set forth in claim 48 wherein said winding current issinusoidal.
 50. The method as set forth in claim 37 wherein saidmagnetic field intensities are peak magnetic surface field intensities.51. The method as set forth in claim 37 wherein said winding layercomprises round wire, square wire, foil sheet, conductive tape ormultiple-strand wire.
 52. A magnetic component made according to themethod of claim
 37. 53. The magnetic component as set forth in claim 52wherein said magnetic component is selected from the group consistingof: coils, inductors, transformers and motors.
 54. The method as setforth in claim 37, further comprising: determining the magnetic fieldintensity at the inner boundary of a second winding layer; determiningthe magnetic field phase at the inner boundary of said second windinglayer; determining the magnetic field intensity at the outer boundary ofsaid second winding layer; determining the magnetic field phase at theouter boundary of said second winding layer; calculating a ratio betweensaid magnetic field intensities of said second winding layer;calculating the relative phase displacement between said phases; andcalculating the desired thickness of said second winding layer as afunction of said ratio and said phase displacement.
 55. The method asset forth in claim 54 wherein said desired thickness of said secondwinding layer is calculated in accordance with the expression:[R ²+1]/R=[cos(B)/cos h(B)+cos h(B)/cos(B)]*cos(Φ) wherein B is a ratiobetween said desired thickness and the skin depth of said second windinglayer, R is said ratio between said magnetic field intensities, and Φ issaid relative phase displacement.
 56. The method as set forth in claim54, wherein said calculation of said desired thickness comprises:computing power dissipation as a function of said ratio between saidmagnetic field intensities for a plurality of predetermined thicknesses;and selecting a desired thickness having a desired power dissipation.57. The method as set forth in claim 56 wherein said power dissipationis computed in accordance with the power loss function, f(H,R,B,Φ. 58.The method as set forth in claim 54, wherein said calculation of saiddesired thickness comprises: computing power dissipation as a functionof said relative phase displacement for a plurality of predeterminedthicknesses; and selecting a desired thickness having a desired powerdissipation.
 59. The method as set forth in claim 58 wherein said powerdissipation is computed in accordance with the power loss function,f(H,R,B,Φ).
 60. The method as set forth in claim 54, wherein saidcalculation of said desired thickness comprises: computing powerdissipation as a function of said ratio between said magnetic fieldintensities and said relative phase displacement for a plurality ofpredetermined thicknesses; and selecting a desired thickness having adesired power dissipation.
 61. The method as set forth in claim 60wherein said power dissipation is computed in accordance with the powerloss function, f(H,R,B,Φ).
 62. The method as set forth in claim 54wherein said calculation of said desired thickness comprises: plottingthe power loss function, f(H,R,B,Φ), for a plurality of predeterminedthicknesses; and selecting a desired thickness having a desired powerdissipation.
 63. The method as set forth in claim 54 wherein saiddesired thickness is the optimal thickness of said first winding layer.64. The method as set forth in claim 54, further comprising:manufacturing a magnetic component having said desired thickness.
 65. Amagnetic component made according to the method of claim
 54. 66. Amethod of calculating the desired thickness of a winding layer for usein a magnetic component, comprising: determining the magnetic fieldintensity at the inner boundary of a first winding layer; determiningthe magnetic field phase at the inner boundary of said first windinglayer; determining the magnetic field intensity at the outer boundary ofsaid first winding layer; determining the magnetic field phase at theouter boundary of said first winding layer; calculating a ratio betweensaid magnetic field intensities; calculating the relative phasedisplacement between said phases; and calculating the desired thicknessof said first winding layer in accordance with the expression:R cos(Φ)sin(B)[sin h(B)[4 cos²(B)+1]+sin h(3B)]−[R ²+1] sin(2B)sinh(2B)=0 wherein B is a ratio between said desired thickness and the skindepth of said first winding layer, R is said ratio between said magneticfield intensities, and Φ is said relative phase displacement.
 67. Themethod as set forth in claim 66, wherein said calculation of saiddesired thickness comprises: computing power dissipation as a functionof said ratio between said magnetic field intensities and said relativephase displacement for a plurality of predetermined thicknesses; andselecting a desired thickness having a desired power dissipation. 68.The method as set forth in claim 67 wherein said power dissipation iscomputed in accordance with the power loss function, f(H,R,B,Φ).
 69. Themethod as set forth in claim 66, wherein said calculation of saiddesired thickness comprises: plotting the power loss function,f(H,R,B,Φ), for a plurality of predetermined thicknesses; and selectinga desired thickness having a desired power dissipation.
 70. The methodas set forth in claim 66 wherein said desired thickness is the optimalthickness of said first winding layer.
 71. The method as set forth inclaim 66, further comprising: manufacturing a magnetic component havingsaid desired thickness.
 72. The method as set forth in claim 66 whereinsaid magnetic field intensities are peak magnetic surface fieldintensities.
 73. A magnetic component made according to the method ofclaim
 66. 74. The magnetic component as set forth in claim 73 whereinsaid magnetic component is selected from the group consisting of: coils,inductors, transformers and motors.
 75. The method as set forth in claim66, further comprising: determining the magnetic field intensity at theinner boundary of a second winding layer; determining the magnetic fieldphase at the inner boundary of said second winding layer; determiningthe magnetic field intensity at the outer boundary of said secondwinding layer; determining the magnetic field phase at the outerboundary of said second winding layer; calculating a ratio between saidmagnetic field intensities of said second winding layer; calculating therelative phase displacement between said phases; and calculating thedesired thickness of said second winding layer as a function of saidratio and said relative phase displacement.
 76. The method as set forthin claim 75 wherein said desired thickness of said second winding layeris calculated in accordance with the expression:R cos(Φ)sin(B)[sin h(B)[4 cos²(B)+1]+sin h(3B)]−[R²+1] sin(2B)sinh(2B)=0.
 77. The method as set forth in claim 75, wherein saidcalculation of said desired thickness of said second winding layercomprises: computing power dissipation as a function of said ratiobetween said magnetic field intensities and said relative phasedisplacement for a plurality of predetermined thicknesses; and selectinga desired thickness of said second winding layer having a desired powerdissipation.
 78. The method as set forth in claim 77 wherein said powerdissipation is computed in accordance with the power loss function,f(H,R,B,Φ).
 79. The method as set forth in claim 75, wherein saidcalculation of said desired thickness of said second winding layercomprises: plotting the power loss function f(H,R,B,Φ), for a pluralityof predetermined thicknesses; and selecting a desired thickness of saidsecond winding layer having a desired power dissipation.
 80. The methodas set forth in claim 75 wherein said desired thickness is the optimalthickness of said first winding layer.
 81. The method as set forth inclaim 75, further comprising: manufacturing a magnetic component havingsaid desired thickness.
 82. The method as set forth in claim 75 whereinsaid magnetic field intensities are peak magnetic surface fieldintensities.
 83. A magnetic component made according to the method ofclaim
 75. 84. A method of calculating the desired thickness of a windinglayer for use in a magnetic component having a winding current,comprising: determining the harmonic components of a winding current;for one or more of said harmonic components: a. determining the magneticfield intensity at the inner boundary of a first winding layer; b.determining the magnetic field phase at the inner boundary of said firstwinding layer; c. determining the magnetic field intensity at the outerboundary of said first winding layer; d. determining the magnetic fieldphase at the outer boundary of said first winding layer; e. calculatinga ratio between said magnetic field intensities; and f. calculating therelative phase displacement between said phases; and determining thedesired thickness of said first winding layer as a function of saidratios and said relative phase displacements.
 85. The method as setforth in claim 84, further comprising: determining the harmonicdissipation in said first winding layer.
 86. The method as set forth inclaim 85 wherein said harmonic dissipation is determined as a functionof said ratios between corresponding magnetic field intensities.
 87. Themethod as set forth in claim 85 wherein said harmonic dissipation isdetermined as a function of said relative phase displacements betweencorresponding phases.
 88. The method as set forth in claim 85 whereinsaid harmonic dissipation is determined as a function of conductorthickness.
 89. The method as set forth in claim 85 wherein said harmonicdissipation is determined as a function of R, Φ and conductor thickness,wherein R is said ratio between corresponding magnetic fieldintensities, and Φ is said relative phase displacement betweencorresponding phases.
 90. The method as set forth in claim 89 whereinsaid harmonic dissipation is determined in accordance with the powerloss function, f(H,R,B,Φ).
 91. The method as set forth in claim 84wherein said desired thickness is determined according to a methodcomprising: iteratively generating a plurality of winding layerthicknesses for said first winding layer; and selecting a desiredthickness having a desired harmonic dissipation.
 92. The method as setforth in claim 91, further comprising: plotting the power loss function,f(H,R,B,Φ), for one or more of said iteratively generated winding layerthicknesses.
 93. The method as set forth in claim 91 wherein saidharmonic dissipation is determined in accordance with the power lossfunction, f(H,R,B,Φ).
 94. The method as set forth in claim 84 whereinsaid harmonic components are determined using Fourier decomposition. 95.The method as set forth in claim 84 wherein said harmonic componentscomprise a DC component.
 96. The method as set forth in claim 84,further comprising: manufacturing a magnetic component having saiddesired thickness.
 97. The method as set forth in claim 84, furthercomprising: identifying the wave form of said winding current.
 98. Themethod as set forth in claim 97 wherein said winding current isnonsinusoidal.
 99. A magnetic component made according to the method ofclaim
 84. 100. The magnetic component as set forth in claim 84 whereinsaid magnetic component is selected from the group consisting of: coils,inductors, transformers and motors.
 101. The method as set forth inclaim 84, further comprising: for one or more of said harmoniccomponents: a. determining the magnetic field intensity at the innerboundary of a second winding layer; b. determining the magnetic fieldphase at the inner boundary of said second winding layer; c. determiningthe magnetic field intensity at the outer boundary of said secondwinding layer; d. determining the magnetic field phase at the outerboundary of said second winding layer; e. calculating a ratio betweensaid magnetic field intensities of said second winding layer; and f.calculating the relative phase displacement between said phases; anddetermining the desired thickness of said second winding layer as afunction of said ratios and said relative phase displacements.
 102. Themethod as set forth in claim 101, further comprising: determining theharmonic dissipation in said second winding layer.
 103. The method asset forth in claim 102, further comprising: selecting a desiredthickness of said first winding layer and a desired thickness of saidsecond winding layer which results in a desired harmonic dissipation.104. The method as set forth in claim 102 wherein said harmonicdissipation is determined as a function of R, Φ and conductor thickness,wherein R is said ratio between corresponding magnetic fieldintensities, and Φ is said relative phase displacement betweencorresponding phases.
 105. The method as set forth in claim 104 whereinsaid harmonic dissipation is determined in accordance with the powerloss function, f(H,R,B,Φ).
 106. The method as set forth in claim 101wherein said desired thickness of said second winding layer isdetermined according to a method comprising: iteratively generating aplurality of predetermined winding layer thicknesses for said secondwinding layer; and selecting a desired thickness of said second windinglayer having a desired harmonic dissipation.
 107. The method as setforth in claim 106, further comprising: plotting the power lossfunction, f(H,R,B,Φ), for one or more of said iteratively generatedwinding layer thicknesses.
 108. The method as set forth in claim 106wherein said harmonic dissipation is determined in accordance with thepower loss function, f(H,R,B,Φ).
 109. The method as set forth in claim101, further comprising: manufacturing a magnetic component having saiddesired thickness.
 110. A magnetic component made according to themethod of claim
 101. 111. A magnetic component, comprising: a windingportion comprising a first winding layer having a thickness defined bythe following expression:cos h(B)=R*cos(B) wherein B is a ratio between said thickness and theskin depth of said first winding layer, and R is the ratio between themagnetic field intensity at the outer boundary of said first windinglayer and the magnetic field intensity at the inner boundary of saidfirst winding layer.
 112. The magnetic component as set forth in claim111, further comprising: a second winding layer having a thicknessdetermined in accordance with said expression.
 113. A magneticcomponent, comprising: a winding portion comprising a first windinglayer having a thickness defined by the following expression:[R²+1]/R=[cos(B)/cos h(B)+cos h(B)/cos(B)]*cos(Φ) wherein B is a ratiobetween said thickness and the skin depth of said first winding layer, Ris said ratio between the magnetic field intensity at the outer boundaryof said first winding layer and the magnetic field intensity at theinner boundary of said first winding layer, and Φ is said relative phasedisplacement between said outer boundary and said inner boundary. 114.The magnetic component as set forth in claim 113, further comprising: asecond winding layer having a thickness determined in accordance withsaid expression.
 115. A magnetic component, comprising: a windingportion comprising a first winding layer having a thickness defined bythe following expression:R cos(Φ)sin(B)[sin h(B)[4 cos²(B)+1]+sin h(3B)]−[R²+1] sin(2B)sinh(2B)=0 wherein B is a ratio between said thickness and the skin depthof said first winding layer, R is said ratio between the magnetic fieldintensity at the outer boundary of said first winding layer and themagnetic field intensity at the inner boundary of said first windinglayer, and Φ is said relative phase displacement between said outerboundary and said inner boundary.
 116. The magnetic component as setforth in claim 115, further comprising: a second winding layer having athickness determined in accordance with said expression.